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I have a body blank. I have my idea for the shape. Also I have this idea for a router jig that will let me pass the router over the top and give the top a small arch. I plan to route the arch after cutting the body shape. Are then any reasons I may want to route the arch first ?

theres always work arounds and that's part of the fun, at least for me.
But Its nice to have a flat surface to get all the other routes in first otherwise you'll always be having to make it level.
Its much harder to work on a curved surface.
so I guess it may be best to do it last.

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You just pick up a chord, go twang, and you're got music. -Sid Vicious

I'd do body shape, top profile (arch), neck pocket last because the bottom of it needs to be parallel with the top - or at least that's how I made a Les Paul.

Kevin Looker

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I'm not a luthier.
I'm just a guy who builds guitars in his basement.
It's better than playing golf.

I agree with William - I try to do everything that requires a flat plane (for a template) or a right angle (for a follower bit) before I do any angles or curves. The exception is the neck pocket on a carved top - that is a reference for all the pickup cavities and the bridge so its important. So if its flat top I would do the body shape, cavities and neck pocket, then do the belly or arm bevels. If you are doing round overs or binding figure out the best way to reference those to the sides.